details

property	value
status	complete
benchmark	thiemann16.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n182.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	3.72413 seconds
cpu usage	3.45391
user time	2.88569
system time	0.568216
max virtual memory	719420.0
max residence set size	15292.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S u:S x:S y:S z:S) (RULES check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(x:S)))) -> check(s(x:S)) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) if(even,x:S,y:S,z:S,u:S) -> plus(timesIter(half(x:S),y:S,half(z:S)),timesIter(half(x:S),y:S,half(s(z:S)))) if(odd,x:S,y:S,z:S,u:S) -> timesIter(p(x:S),y:S,u:S) if(zero,x:S,y:S,z:S,u:S) -> z:S p(0) -> 0 p(s(x:S)) -> x:S plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) times(x:S,y:S) -> timesIter(x:S,y:S,0) timesIter(x:S,y:S,z:S) -> if(check(x:S),x:S,y:S,z:S,plus(z:S,y:S)) ) Problem 1: Innermost Equivalent Processor: -> Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(x:S)))) -> check(s(x:S)) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) if(even,x:S,y:S,z:S,u:S) -> plus(timesIter(half(x:S),y:S,half(z:S)),timesIter(half(x:S),y:S,half(s(z:S)))) if(odd,x:S,y:S,z:S,u:S) -> timesIter(p(x:S),y:S,u:S) if(zero,x:S,y:S,z:S,u:S) -> z:S p(0) -> 0 p(s(x:S)) -> x:S plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) times(x:S,y:S) -> timesIter(x:S,y:S,0) timesIter(x:S,y:S,z:S) -> if(check(x:S),x:S,y:S,z:S,plus(z:S,y:S)) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: CHECK(s(s(s(x:S)))) -> CHECK(s(x:S)) HALF(s(s(x:S))) -> HALF(x:S) IF(even,x:S,y:S,z:S,u:S) -> HALF(s(z:S)) IF(even,x:S,y:S,z:S,u:S) -> HALF(x:S) IF(even,x:S,y:S,z:S,u:S) -> HALF(z:S) IF(even,x:S,y:S,z:S,u:S) -> PLUS(timesIter(half(x:S),y:S,half(z:S)),timesIter(half(x:S),y:S,half(s(z:S)))) IF(even,x:S,y:S,z:S,u:S) -> TIMESITER(half(x:S),y:S,half(s(z:S))) IF(even,x:S,y:S,z:S,u:S) -> TIMESITER(half(x:S),y:S,half(z:S)) IF(odd,x:S,y:S,z:S,u:S) -> P(x:S) IF(odd,x:S,y:S,z:S,u:S) -> TIMESITER(p(x:S),y:S,u:S) PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) TIMES(x:S,y:S) -> TIMESITER(x:S,y:S,0) TIMESITER(x:S,y:S,z:S) -> CHECK(x:S) TIMESITER(x:S,y:S,z:S) -> IF(check(x:S),x:S,y:S,z:S,plus(z:S,y:S)) TIMESITER(x:S,y:S,z:S) -> PLUS(z:S,y:S) -> Rules: check(0) -> zero check(s(0)) -> odd check(s(s(0))) -> even check(s(s(s(x:S)))) -> check(s(x:S)) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) if(even,x:S,y:S,z:S,u:S) -> plus(timesIter(half(x:S),y:S,half(z:S)),timesIter(half(x:S),y:S,half(s(z:S)))) if(odd,x:S,y:S,z:S,u:S) -> timesIter(p(x:S),y:S,u:S) if(zero,x:S,y:S,z:S,u:S) -> z:S p(0) -> 0 p(s(x:S)) -> x:S plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) times(x:S,y:S) -> timesIter(x:S,y:S,0) timesIter(x:S,y:S,z:S) -> if(check(x:S),x:S,y:S,z:S,plus(z:S,y:S)) Problem 1: SCC Processor: -> Pairs: CHECK(s(s(s(x:S)))) -> CHECK(s(x:S)) HALF(s(s(x:S))) -> HALF(x:S) IF(even,x:S,y:S,z:S,u:S) -> HALF(s(z:S)) IF(even,x:S,y:S,z:S,u:S) -> HALF(x:S) IF(even,x:S,y:S,z:S,u:S) -> HALF(z:S) IF(even,x:S,y:S,z:S,u:S) -> PLUS(timesIter(half(x:S),y:S,half(z:S)),timesIter(half(x:S),y:S,half(s(z:S)))) IF(even,x:S,y:S,z:S,u:S) -> TIMESITER(half(x:S),y:S,half(s(z:S))) IF(even,x:S,y:S,z:S,u:S) -> TIMESITER(half(x:S),y:S,half(z:S)) IF(odd,x:S,y:S,z:S,u:S) -> P(x:S) IF(odd,x:S,y:S,z:S,u:S) -> TIMESITER(p(x:S),y:S,u:S) PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) TIMES(x:S,y:S) -> TIMESITER(x:S,y:S,0) popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to TRS Standard